Subcategory display format on Categories page

At the moment there is an inconsistency between the way subcategories display in the setting “desktop category page style” : “Boxes with Subcategories” and all of the other options which display the list of subcategories.
In the Boxes option then the colour blobs and the lock symbols are not displayed but if a subcategory has logo defined then a mini version of the logo gets displayed before the title:
In the other options the subcategory logo is never displayed but the locks (if appropriate) and colour blobs are displayed:

I really like having the mini logo displayed in the boxes (which is my preferred option for the categories page), but I would like to have the locks also there, and if no logo exists logo then the colour blob instead.
I’d also like it to be an option to display the subcategory logo in other views in place of the colour blob.

Since this may take a while before this would be agreed, let alone picked up, as a desirable feature my thought is to start by creating a theme component to address this. But I have little idea where to start - can anyone give me a clue where the two conflicting formats for the subcategory list are defined and how to combine the desirable features of both? Would it be even feasible to do this as a theme component?